The invention relates in general to functional MR imaging, and in particular to fMRI signal analysis.
Changes in neuronal activity responsive to the accomplishment of mental and/or physical tasks, such as touching a finger to thumb, are accompanied by physiological changes in regions of the brain associated with and/or controlling the activity. Physiological changes such as cerebral blood flow, blood volume, blood oxygenation and/or metabolism, occurring in such a region of the brain are made visible by functional MR imaging (fMRI).
A typical fMRI session comprises the following steps: (a) stimulating a subject (e.g. by asking him to perform, preferably, a periodic task, usually a task targeting a particular brain region, or be subjected to a periodic visual/audio/tactile stimuli), (b) MR imaging a region of the brain supposed to be involved in the accomplishment of that task, and (c) analyzing a time series of acquired images to determine physiological changes in the brain region.
Often, the signal to noise ratio of fMRI images is poor, so a synchronized detection method of image analysis is preferably used. It is expected that the physiological changes mirror the activity that the subject performs. Thus, the images are analyzed based on expected correlation between variations in pixel values in the analyzed regions and the activity performed by the subject. Generally, however, there is a delay between the performance of the activity and a change in the physiological variable. This delay, as well as the exact response of the pixel value to the activity, are generally not known in advance.
Reference is now made to FIG. 1 which shows a flow chart for a general fMRI data analysis. Due to the repetitive nature of the activity performed by the subject and the dependence of the physiological changes on the activity, many aspects of the process are best described as a time varying periodic function. An xe2x80x9con-off-on-off-onxe2x80x9d stimulation (or activity) paradigm 20, such as touching a finger to thumb, may be represented by an activation function, where on""s are 1s and off""s are 0s. Activity 20 induces neuronal activity 22. As a result of neuronal activity 22, certain brain tissues react (24), for example blood vessels open to bring in oxygenated blood and/or neurons use up oxygen in a blood stream. These effects are represented by Fxcex1(r, tk) (24), where Fxcex1(r, tk) is the possibly non-linear response of the brain, as a function of location and time, to the activity. Fxcex2 is the possibly non-linear response of a pixel, in the image, to the response of the brain Fxcex1(r, tk) as imaged by the MR imager (30). qij(tk)=Fxcex2(Fxcex1(r, tk)) (34), is a pixel, (pixel ij); response function which relates variations in (ij)th pixel intensity, as imaged by the MR imager in step 30, and/or other image parameters, such as pixel phase, to physiological changes 24. In the above described brain and pixel responses, tk represents the discretization of time, which corresponds to the instant at which each MR image is acquired. Typically, tk=k*xcex94t, where xcex94t is the time difference between consecutive images. Alternatively, the images may be non equally spaced in time. Subscript ij represents the discretization of locality r. Typically, image registration (alignment) is performed so that a same image pixel corresponds to a same brain volume over an entire series of images. Typically, the pixel response function is difficult to detect and/or otherwise analyze because of the above mentioned low signal-to-noise ratio. A small signal and two different noise sources, instrumental noise 38, and physiological fluctuations 40, contribute to this low signal-to-noise ratio.
In a typical fMRI study, the activity of a brain tissue may be assessed by comparing the pixel response function qij(tk) 34, and the activation function. As it is difficult to detect directly pixel activity from the collected data because of the very low signal-to-noise ratio, the detection is performed synchronously by correlation, 42, between the pixel response qij(tk), embedded in noise and a certain detection (or reference) function, 36, which is thought to best fit the detection task. The synchronously detected pixel response function, qij(tk), is then compared with the activation function.
According to the correlation results 44, which are reflected by the correlation coefficient(s) xcfx81ij, the analyzed pixel is said to have no activity 49, if the correlation is poor, or to be active 50, if the correlation is high. Intermediary correlation values may point to different levels of activity of the analyzed biological tissues contained in a voxel.
In conventional fMRI, the detection (or reference) function, 36, which is thought to best fit the detection task is guessed at. The most commonly guessed detection functions are square pulses, which in fact are identical to the repetitive part of the activation function describing an xe2x80x9con-off-on-offxe2x80x9d task, a sinusoidal pulse or an exponential pulse which are close to the square pulse. The drawback of this method is that there is no physiological or other objective basis for guessing a detection function, that a guessed detection function may be delayed relative to the activation function and that the activation function is usually not a square function.
xe2x80x9cTime Course EPI of Human Brain Function during Task Activationxe2x80x9d by Peter A. Bandettini et al., Magnetic Resonance in Medicine, Vol. 25, p. 390-397 (1992); xe2x80x9cProcessing Strategies for Time-Course Data sets in Functional MRI of the Human Brainxe2x80x9d, by Peter A. Bandettini et al., Magnetic Resonance in Medicine, Vol. 30, p. 161-173 (1993) and xe2x80x9cReal-Time Functional Magnetic Resonance Imagingxe2x80x9d, by Robert W. Cox et al., Magnetic Resonance in Medicine, Vol. 33, p. 230-236 (1995) all of which are incorporated herein by reference, deal with fMRI signal processing using a guessed detection function.
In xe2x80x9cProcessing Strategies for Time-Course Data sets in Functional MRI of the Human Brainxe2x80x9d, Bandettini et al. use a time-course function in a given pixel as detection (reference) function in fMRI signal analysis. This detection (reference) function may be an experimental time-course function of some particular pixel or a time-course function which is linearly filtered from several experimental time-course functions. This detection (reference) function is then correlated with time-course functions in other pixels. Linear filtering such as performed by Peter, A. Bandettini may eliminate local differences. But as Bandettini""s detection function is an experimental time-course function f in some particular pixel or an average of several experimental f""s, the linear filtering, as applied by Bandettini, does not ensure the obtaintion of a detection function which is most appropriate in the synchronous detection of a pixel response qij(tk), embedded in noise.
In the claims and specification of the present application each of the verbs, xe2x80x9ccomprisexe2x80x9d and xe2x80x9cincludexe2x80x9d and conjugates thereof are used to convey that the object or objects of the verb are not necessarily a listing of all the components, elements or parts of the subject or subjects of the verb.
One aspect of some preferred embodiments of the present invention relates to calculating a detection function for use in synchronous detection in fMRI signal analysis. Preferably, the detection function for fMRI data analysis is derived from the fMRI data itself. Some preferred embodiments of the present invention relate to a method of determining a detection function by non-linear filtering, preferably, from response functions of a plurality of pixels situated in a region of interest whose behavior is studied. More preferably, the non-linear filtering method uses eigen analysis in order to separate at least two subspaces, namely signal subspace (one or more) and noise subspace, within the space of all the fMRI time course signals. Preferably, the final result of the method is the obtaintion of basis vectors that span these signal and noise subspaces. Preferably, the basis vectors of the signal subspace(s) are used as the detection function. More generally, other non-linear filtering methods, such as median filtering, may also be used to calculate a detection function.
One way of separating the signal and noise subspaces is the well known Gram-Schmidt orthogonalization, which may, in some cases be numerically problematic. Therefore, in some preferred embodiments of the present invention the singular value decomposition method is used in order to separate the signal and noise subspaces.
In SVD calculations, an Mxc3x97N matrix [A], whose elements are the intensity values of the pixels of MR images, is constructed from pixel response functions qij(tk) related to a region of the brain. In matrix [A], M=number of pixels and N=number of images. In SVD calculations, matrix [A] is decomposed into a product of three matrices, namely [U], [V] and [W]. In a preferred embodiment of the present invention, a calculated detection (reference) function {overscore (q)}(tk) 36, is obtained from the SVD calculations. As this calculated (reference) detection function {overscore (q)}(tk), is directly generated from the studied area, it better represents the response qij(tk), of a studied pixel in a more competent way than does a guessed function. In SVD calculations, the calculated detection function is given by the column of matrix [U] which has the same index as the column of matrix [W] which contains the xcfx89j element having the greatest magnitude. The matrix [W] may have more than one xcfx89j element with substantially greater magnitude compared to the other xcfx89j elements. As a consequence, the calculated detection (reference) function {overscore (q)}(tk) may also be defined by more than one column of matrix [U] with the same indexes as the columns of [W] with the largest (xcfx89j elements.
Another aspect of some preferred embodiments of the present invention relates to the detection of two, or more, overlapping pixel responses functions; for example, in case a subject is subjected to periodic electric stimuli on a finger which is performing a voluntary activation task.
There is therefore provided, in accordance with a preferred embodiment of the present invention, a method for MRI signal analysis of an area of a biological tissue comprising:
a) providing a biological tissue, wherein physiological activity is taking place in an area thereof;
b) acquiring sequential magnetic resonance images, at least during a portion of time in which said physiological activity is taking place, of said area and of at least a portion of the tissue in a vicinity of the area;
c) constructing, responsive to at least one pixel-related parameter value of said images, a pixel parameter space; and
d) separating the pixel parameter space into at least two subspaces.
There is also provided, in accordance with a preferred embodiment of the present invention, a method for functional MRI (fMRI) signal analysis of an area of the brain comprising:
a) invoking neuronal activity in an area of the brain of a subject;
b) acquiring sequential magnetic resonance images, at least during a portion of time in which said area of the brain of a subject is activated, of said area and of at least a portion of the brain in a vicinity of the area;
c) constructing, responsive to at least one pixel-related parameter value of said images, a pixel parameter space; and
d) applying non linear filtering to said pixel parameter space, wherein said non linear filtering separates said pixel parameter space into at least two subspaces.
Preferably, said at least one pixel-related parameter comprises a pixel magnitude value. Preferably, said at least two subspaces comprise a signal subspace and a noise subspace. Preferably, said non linear filtering uses singular value decomposition. Preferably, said magnitude values are arranged in a matrix.
There is also provided, in accordance with a preferred embodiment of the present invention, a method comprising decomposing the matrix of magnitude values into a product of a plurality of matrices, the columns of one matrix of the plurality of matrices comprising a plurality of basis vectors which span said at least two subspaces. Preferably, said at least two subspaces comprise a signal subspace and a noise subspace. More preferably, one basis vector spans said signal subspace. In some preferred embodiments of the present invention, two or more basis vectors span said signal subspace.
There is also provided, in accordance with a preferred embodiment of the present invention, a method comprising detecting temporal variations in said area over a sequence of images using a synchronous detection fiction. Preferably, said basis vector is used as a detection function. In some preferred embodiments of the present invention, said detection comprises synchronous detection. Preferably said basis vectors are used as synchronous detection functions.
There is also provided, in accordance with a preferred embodiment of the present invention, a method comprising:
a) repeating said synchronous detection on all the pixels related to an area of interest in the brain;
b) obtaining, for each said synchronous detection, at least one detection indicator which indicates a quality of said synchronous detection; and
c) identifying those of said at least one detection indicator which meet at least one certain criterion.
Preferably, said method also comprises:
a) deriving a plurality of detection functions from image portions of a region of the brain in the vicinity of the area in said sequential images;
b) synchronously detecting temporal variations in said area, over a sequence of images, using synchronous detection:
c) obtaining a plurality of detection indicator values from said synchronous detection, for a plurality of pixels related to an area of interest in the brain;
d) constructing a vector from detection indicator values associated with a single pixel, for each pixel of said plurality of pixels;
e) calculating the magnitude of each of said vectors; and
f) identifying those of said magnitudes which meet at least one certain criterion.
g) deriving a vector phase from each of said vectors.
Preferably, a delay between the neuronal activity and a cause which invoked it using said phase of each vector is detected from said vector phase. Additionally, at least a relative intensity and/or an absolute intensity of said neuronal activity is determined from said magnitude of each vector. Preferably, said neuronal activity in said area of the brain of a subject is periodic. In some preferred embodiments of the present invention at least one of said MR images is acquired after a cession of said invoking of neuronal activity. Preferably, trends unrelated to said neuronal activity are removed before said applying non linear filtering.
In some other preferred embodiments of the present invention, at least a second activity simultaneous with the first activity is also invoked. Preferably, signals related to said at least two invoked activities are independently extracting.
There is also provided, in accordance with a preferred embodiment of the present invention, a method for functional MRI (fMRI) signal analysis of an area of the brain comprising:
a) invoking neuronal activity in an area of the brain of a subject;
b) acquiring sequential magnetic resonance images, at least during a portion of time in which said area of the brain of a subject is activated, of said area and of at least a portion of the brain in a vicinity of the area;
c) registering said sequential images;
d) constructing a pixel parameter space, responsive to pixel magnitude values in said images;
e) removing, from said space, at least one trend unrelated to said neuronal activity;
f) arranging said trend-removed magnitude values in a matrix;
g) separating said pixel parameter space into at least two subspaces, using singular value decomposition, such that said matrix is decomposed into a product of a plurality of matrices, the columns of one matrix of the plurality of matrices comprising a plurality of basis vectors which span said at least two subspaces;
h) identifying said at least two subspaces as a signal subspace and as a noise subspace;
i) selecting at least one of said basis vectors which spans said signal subspace;
j) detecting variations in said area of the brain over a sequence of images using said at least one vector as a synchronous detection function, for all the pixels related to an area of interest in the brain;
k) obtaining, for each said synchronous detection, at least one detection indicator which indicates a quality of said synchronous detection.
Preferably, said at least one basis vector which spans said signal subspace comprises at least two independent basis vectors.
In some preferred embodiments of the present invention, a plurality of detection indicators are obtained for said each pixel, then a vector is constructed from said detection indicators and finally, the magnitude of each said constructed vector is calculated.